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If vectors A and B are given by $A = 5 \hat{i} + 6 \hat{j} + 3 \hat{k} a n d B = 6 \hat{i} - 2 \hat{j} - 6 \hat{k} .$ Which of the following is /are correct?

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Product $\vec{A}$ × $\vec{B}$ is the same as $\vec{B}$ × $\vec{A}$

$\vec{A}$ and $\vec{B}$ are mutually perpendicular

The magnitude of $\vec{A}$ and $\vec{B}$ are equal

The magnitude of $\vec{A}$ . $\vec{B}$ is zero

answer is A, D.

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Detailed Solution

Here, $A . B = (5 \hat{i} + 6 \hat{j} + 3 \hat{k}) . (6 \hat{i} - 2 \hat{j} - 6 \hat{k}) = 0$

So, A is perpendicular to B and A is not equal to A × B, as cross product of two vectors in anticommutative. The magnitude of A is $\sqrt{70} a n d B i s \sqrt{76}$

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